TSTP Solution File: NUM673^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM673^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.COiCWGA17i true
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:43:20 EDT 2023
% Result : Theorem 62.54s 8.64s
% Output : Refutation 62.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 86
% Syntax : Number of formulae : 168 ( 72 unt; 28 typ; 0 def)
% Number of atoms : 854 ( 215 equ; 55 cnn)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 2089 ( 278 ~; 80 |; 0 &;1344 @)
% ( 0 <=>; 262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 7 con; 0-3 aty)
% ( 125 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 387 ( 277 ^; 110 !; 0 ?; 387 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
thf(orec3_type,type,
orec3: $o > $o > $o > $o ).
thf(nat_type,type,
nat: $i ).
thf(lessis_type,type,
lessis: $i > $i > $o ).
thf(and3_type,type,
and3: $o > $o > $o > $o ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(non_type,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(l_some_type,type,
l_some: $i > ( $i > $o ) > $o ).
thf('#sk8033_type',type,
'#sk8033': $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(l_ec_type,type,
l_ec: $o > $o > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(ec3_type,type,
ec3: $o > $o > $o > $o ).
thf('#sk8034_type',type,
'#sk8034': $i ).
thf(d_and_type,type,
d_and: $o > $o > $o ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(diffprop_type,type,
diffprop: $i > $i > $i > $o ).
thf('#sk7435_type',type,
'#sk7435': $i > $i > $i ).
thf(n_some_type,type,
n_some: ( $i > $o ) > $o ).
thf(l_or_type,type,
l_or: $o > $o > $o ).
thf('#form7436_type',type,
'#form7436': $i > $i > $o ).
thf(d_not_type,type,
d_not: $o > $o ).
thf('#sk8032_type',type,
'#sk8032': $i ).
thf(iii_type,type,
iii: $i > $i > $o ).
thf(or3_type,type,
or3: $o > $o > $o > $o ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
thf('0',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('1',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('2',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'1']) ).
thf('3',plain,
( n_is
= ( e_is @ nat ) ),
define([status(thm)]) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).
thf('4',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('5',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('6',plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_all_of,'5']) ).
thf('7',plain,
( all_of
= ( ^ [V_1: $i > $o,V_2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ V_1 )
=> ( V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(satz6,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ( n_pl @ X4 @ X6 )
= ( n_pl @ X6 @ X4 ) ) ) ) ).
thf(zip_derived_cl132,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ Y1 )
= ( n_pl @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1717,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X2 @ Y0 )
= ( n_pl @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl1718,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X2 @ Y0 )
= ( n_pl @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1717]) ).
thf(zip_derived_cl1719,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( ( n_pl @ X2 @ X4 )
= ( n_pl @ X4 @ X2 ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1718]) ).
thf(zip_derived_cl1720,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( ( n_pl @ X2 @ X4 )
= ( n_pl @ X4 @ X2 ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1719]) ).
thf(zip_derived_cl1721,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( ( n_pl @ X2 @ X4 )
= ( n_pl @ X4 @ X2 ) )
| ~ ( in @ X2 @ nat ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1720]) ).
thf(zip_derived_cl1721_001,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( ( n_pl @ X2 @ X4 )
= ( n_pl @ X4 @ X2 ) )
| ~ ( in @ X2 @ nat ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1720]) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).
thf('8',plain,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_diffprop,'3','1']) ).
thf('9',plain,
( diffprop
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X0: $i,X1: $i > $o] :
( d_not
@ ( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ( non @ X0 @ X1 ) ) ) ) ) ).
thf(def_non,axiom,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
thf(def_imp,axiom,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ) ).
thf('10',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('11',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('12',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'11']) ).
thf('13',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('14',plain,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_non,'13','11']) ).
thf('15',plain,
( non
= ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('16',plain,
( l_some
= ( ^ [X0: $i,X1: $i > $o] :
( d_not
@ ( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ( non @ X0 @ X1 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_some,'15','13','11','7','5']) ).
thf('17',plain,
( l_some
= ( ^ [V_1: $i,V_2: $i > $o] :
( d_not
@ ( all_of
@ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
@ ( non @ V_1 @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('18',plain,
( n_some
= ( l_some @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_some,'17','15','13','11','7','5']) ).
thf('19',plain,
( n_some
= ( l_some @ nat ) ),
define([status(thm)]) ).
thf('20',plain,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_29_ii,'9','19','3','1','17','15','13','11','7','5']) ).
thf('21',plain,
( d_29_ii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz19d,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) ) ) ) ) ).
thf(zf_stmt_1,conjecture,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X10 ) ) )
=> ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( ( n_pl @ X8 @ X4 )
!= ( n_pl @ ( n_pl @ X8 @ X6 ) @ X12 ) ) ) ) ) ) ) ).
thf(zf_stmt_2,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X10 ) ) )
=> ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( ( n_pl @ X8 @ X4 )
!= ( n_pl @ ( n_pl @ X8 @ X6 ) @ X12 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl168,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y3 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( n_pl @ Y2 @ Y0 )
!= ( n_pl @ ( n_pl @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl6312,plain,
~ ( ( in @ '#sk8032' @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( '#sk8032'
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_pl @ Y1 @ '#sk8032' )
!= ( n_pl @ ( n_pl @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl168]) ).
thf(zip_derived_cl6314,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( '#sk8032'
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_pl @ Y1 @ '#sk8032' )
!= ( n_pl @ ( n_pl @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6312]) ).
thf(zip_derived_cl6315,plain,
~ ( ( in @ '#sk8033' @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk8032'
!= ( n_pl @ '#sk8033' @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ '#sk8032' )
!= ( n_pl @ ( n_pl @ Y0 @ '#sk8033' ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6314]) ).
thf(zip_derived_cl6317,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk8032'
!= ( n_pl @ '#sk8033' @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ Y0 @ '#sk8032' )
!= ( n_pl @ ( n_pl @ Y0 @ '#sk8033' ) @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6315]) ).
thf(zip_derived_cl6318,plain,
~ ( ( in @ '#sk8034' @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8032'
!= ( n_pl @ '#sk8033' @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ '#sk8034' @ '#sk8032' )
!= ( n_pl @ ( n_pl @ '#sk8034' @ '#sk8033' ) @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6317]) ).
thf(zip_derived_cl6320,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8032'
!= ( n_pl @ '#sk8033' @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ '#sk8034' @ '#sk8032' )
!= ( n_pl @ ( n_pl @ '#sk8034' @ '#sk8033' ) @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6318]) ).
thf(zip_derived_cl6322,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ '#sk8034' @ '#sk8032' )
!= ( n_pl @ ( n_pl @ '#sk8034' @ '#sk8033' ) @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6320]) ).
thf(def_orec3,axiom,
( orec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ) ).
thf(def_ec3,axiom,
( ec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ) ).
thf(def_and3,axiom,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ) ).
thf('22',plain,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_ec,'13','11']) ).
thf('23',plain,
( l_ec
= ( ^ [V_1: $o,V_2: $o] : ( imp @ V_1 @ ( d_not @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('24',plain,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_and,'23','13','11']) ).
thf('25',plain,
( d_and
= ( ^ [V_1: $o,V_2: $o] : ( d_not @ ( l_ec @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('26',plain,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_and3,'25','23','13','11']) ).
thf('27',plain,
( and3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( d_and @ V_1 @ ( d_and @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('28',plain,
( ec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_ec3,'27','25','23','13','11']) ).
thf('29',plain,
( ec3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( and3 @ ( l_ec @ V_1 @ V_2 ) @ ( l_ec @ V_2 @ V_3 ) @ ( l_ec @ V_3 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(def_or3,axiom,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ) ).
thf('30',plain,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_or,'13','11']) ).
thf('31',plain,
( l_or
= ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('32',plain,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_or3,'31','13','11']) ).
thf('33',plain,
( or3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( l_or @ V_1 @ ( l_or @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('34',plain,
( orec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_orec3,'29','27','33','31','25','23','13','11']) ).
thf('35',plain,
( orec3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( d_and @ ( or3 @ V_1 @ V_2 @ V_3 ) @ ( ec3 @ V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(satz9,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( orec3 @ ( n_is @ X0 @ X1 )
@ ( n_some
@ ^ [X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )
@ ( n_some
@ ^ [X2: $i] : ( n_is @ X1 @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ~ ( ( ( X4 != X6 )
=> ( ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X8 ) ) )
=> ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X10 ) ) ) ) )
=> ( ( ( X4 = X6 )
=> ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X12 ) ) ) )
=> ( ( ~ ! [X14: $i] :
( ( in @ X14 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X14 ) ) )
=> ! [X16: $i] :
( ( in @ X16 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X16 ) ) ) )
=> ~ ( ~ ! [X18: $i] :
( ( in @ X18 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X18 ) ) )
=> ( X4 != X6 ) ) ) ) ) ) ) ).
thf(zip_derived_cl137,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( (~)
@ ( ( ( Y0 != Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( Y0 != Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl5555,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( (~)
@ ( ( ( X2 != Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( X2 = Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( X2 != Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl5556,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( (~)
@ ( ( ( X2 != Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( X2 = Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( X2 != Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5555]) ).
thf(zip_derived_cl5557,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( (~)
@ ( ( ( X2 != X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5556]) ).
thf(zip_derived_cl5558,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ~ ( ( ( X2 != X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5557]) ).
thf(zip_derived_cl5560,plain,
! [X2: $i,X4: $i] :
( ~ ( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5558]) ).
thf(zip_derived_cl5562,plain,
! [X2: $i,X4: $i] :
( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5560]) ).
thf(zip_derived_cl5566,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5562]) ).
thf(zip_derived_cl5570,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl5566]) ).
thf(zip_derived_cl5571,plain,
! [X4: $i] :
( ~ ( in @ X4 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5570]) ).
thf(zip_derived_cl5572,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7436' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf(def_iii,axiom,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ).
thf('36',plain,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_iii,'9','19','3','1','17','15','13','11','7','5']) ).
thf('37',plain,
( iii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('38',plain,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_lessis,'37','9','19','3','1','17','15','31','13','11','7','5']) ).
thf('39',plain,
( lessis
= ( ^ [V_1: $i,V_2: $i] : ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz10e,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_not @ ( d_29_ii @ X0 @ X1 ) )
=> ( lessis @ X0 @ X1 ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X8 ) ) )
=> ( ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X10 ) ) )
=> ( X4 = X6 ) ) ) ) ) ).
thf(zip_derived_cl149,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl5487,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) )
=> ( X2 = Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl5488,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) )
=> ( X2 = Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5487]) ).
thf(zip_derived_cl5489,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
=> ( X2 = X4 ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5488]) ).
thf(zip_derived_cl5490,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
=> ( X2 = X4 ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5489]) ).
thf(zip_derived_cl5491,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
=> ( X2 = X4 ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5490]) ).
thf(zip_derived_cl5492,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ ( '#sk7435' @ X2 @ X4 ) @ nat )
=> ( X2
!= ( n_pl @ X4 @ ( '#sk7435' @ X2 @ X4 ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5491]) ).
thf(zip_derived_cl5493,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk7435' @ X2 @ X4 ) @ nat )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
=> ( X2 = X4 ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5492]) ).
thf(zip_derived_cl5495,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
| ( X2 = X4 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( in @ ( '#sk7435' @ X2 @ X4 ) @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5493]) ).
thf(zip_derived_cl5498,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
| ( X2 = X4 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( in @ ( '#sk7435' @ X2 @ X4 ) @ nat ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl5495]) ).
thf(zip_derived_cl5499,plain,
! [X2: $i,X4: $i] :
( ( '#form7436' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6324,plain,
'#form7436' @ ( n_pl @ '#sk8034' @ '#sk8033' ) @ ( n_pl @ '#sk8034' @ '#sk8032' ),
inference(renaming,[status(thm)],[zip_derived_cl6322,zip_derived_cl5572,zip_derived_cl5499]) ).
thf(zip_derived_cl6604,plain,
( ( '#form7436' @ ( n_pl @ '#sk8033' @ '#sk8034' ) @ ( n_pl @ '#sk8034' @ '#sk8032' ) )
| ~ ( in @ '#sk8033' @ nat )
| ~ ( in @ '#sk8034' @ nat ) ),
inference('sup+',[status(thm)],[zip_derived_cl1721,zip_derived_cl6324]) ).
thf(zip_derived_cl6316,plain,
in @ '#sk8033' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6315]) ).
thf(zip_derived_cl6319,plain,
in @ '#sk8034' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6318]) ).
thf(zip_derived_cl6614,plain,
'#form7436' @ ( n_pl @ '#sk8033' @ '#sk8034' ) @ ( n_pl @ '#sk8034' @ '#sk8032' ),
inference(demod,[status(thm)],[zip_derived_cl6604,zip_derived_cl6316,zip_derived_cl6319]) ).
thf(zip_derived_cl6632,plain,
( ( '#form7436' @ ( n_pl @ '#sk8033' @ '#sk8034' ) @ ( n_pl @ '#sk8032' @ '#sk8034' ) )
| ~ ( in @ '#sk8032' @ nat )
| ~ ( in @ '#sk8034' @ nat ) ),
inference('sup+',[status(thm)],[zip_derived_cl1721,zip_derived_cl6614]) ).
thf(zip_derived_cl6313,plain,
in @ '#sk8032' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6312]) ).
thf(zip_derived_cl6319_002,plain,
in @ '#sk8034' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6318]) ).
thf(zip_derived_cl6642,plain,
'#form7436' @ ( n_pl @ '#sk8033' @ '#sk8034' ) @ ( n_pl @ '#sk8032' @ '#sk8034' ),
inference(demod,[status(thm)],[zip_derived_cl6632,zip_derived_cl6313,zip_derived_cl6319]) ).
thf(satz19a,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X10 ) ) )
=> ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( ( n_pl @ X4 @ X8 )
!= ( n_pl @ ( n_pl @ X6 @ X8 ) @ X12 ) ) ) ) ) ) ) ).
thf(zip_derived_cl165,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y3 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( n_pl @ Y0 @ Y2 )
!= ( n_pl @ ( n_pl @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl7478,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_pl @ X2 @ Y1 )
!= ( n_pl @ ( n_pl @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl7479,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_pl @ X2 @ Y1 )
!= ( n_pl @ ( n_pl @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7478]) ).
thf(zip_derived_cl7480,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ X2 @ Y0 )
!= ( n_pl @ ( n_pl @ X4 @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7479]) ).
thf(zip_derived_cl7481,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_pl @ X2 @ Y0 )
!= ( n_pl @ ( n_pl @ X4 @ Y0 ) @ Y1 ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7480]) ).
thf(zip_derived_cl7482,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X2 @ X6 )
!= ( n_pl @ ( n_pl @ X4 @ X6 ) @ Y0 ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7481]) ).
thf(zip_derived_cl7483,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ nat )
| ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X2 @ X6 )
!= ( n_pl @ ( n_pl @ X4 @ X6 ) @ Y0 ) ) ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7482]) ).
thf(zip_derived_cl7484,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X2 @ X6 )
!= ( n_pl @ ( n_pl @ X4 @ X6 ) @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X6 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7483]) ).
thf(zip_derived_cl5572_003,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7436' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5499_004,plain,
! [X2: $i,X4: $i] :
( ( '#form7436' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7485,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( '#form7436' @ X4 @ X2 )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ X2 @ X6 )
!= ( n_pl @ ( n_pl @ X4 @ X6 ) @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl7484,zip_derived_cl5572,zip_derived_cl5499]) ).
thf(zip_derived_cl5572_005,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7436' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5499_006,plain,
! [X2: $i,X4: $i] :
( ( '#form7436' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7486,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#form7436' @ ( n_pl @ X4 @ X6 ) @ ( n_pl @ X2 @ X6 ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X6 @ nat )
| ( '#form7436' @ X4 @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl7485,zip_derived_cl5572,zip_derived_cl5499]) ).
thf(zip_derived_cl7507,plain,
( ( '#form7436' @ '#sk8033' @ '#sk8032' )
| ~ ( in @ '#sk8034' @ nat )
| ~ ( in @ '#sk8033' @ nat )
| ~ ( in @ '#sk8032' @ nat ) ),
inference('sup-',[status(thm)],[zip_derived_cl6642,zip_derived_cl7486]) ).
thf(zip_derived_cl6321,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8032'
!= ( n_pl @ '#sk8033' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6320]) ).
thf(zip_derived_cl5572_007,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7436' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5499_008,plain,
! [X2: $i,X4: $i] :
( ( '#form7436' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6323,plain,
~ ( '#form7436' @ '#sk8033' @ '#sk8032' ),
inference(renaming,[status(thm)],[zip_derived_cl6321,zip_derived_cl5572,zip_derived_cl5499]) ).
thf(zip_derived_cl6319_009,plain,
in @ '#sk8034' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6318]) ).
thf(zip_derived_cl6316_010,plain,
in @ '#sk8033' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6315]) ).
thf(zip_derived_cl6313_011,plain,
in @ '#sk8032' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6312]) ).
thf(zip_derived_cl7542,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl7507,zip_derived_cl6323,zip_derived_cl6319,zip_derived_cl6316,zip_derived_cl6313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM673^4 : TPTP v8.1.2. Released v7.1.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.COiCWGA17i true
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:38:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.22/0.36 % Running in HO mode
% 0.22/0.65 % Total configuration time : 828
% 0.22/0.65 % Estimated wc time : 1656
% 0.22/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.79 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.02/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.02/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 37.70/5.51 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 62.54/8.64 % Solved by lams/35_full_unif4.sh.
% 62.54/8.64 % done 688 iterations in 7.863s
% 62.54/8.64 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 62.54/8.64 % SZS output start Refutation
% See solution above
% 62.54/8.64
% 62.54/8.64
% 62.54/8.64 % Terminating...
% 63.20/8.77 % Runner terminated.
% 63.20/8.77 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------